Activity II: The Polynomial TrainThis is actually a twist on what I really did, but I think I will do it this way next time.

I'd start with a constant function (f(x)=1 in the example below) graphed usingDesmo's calculator and ask a student to add a term to the function so that it would ________ to the left and ________ to the right. The next student would be asked to add another term in order to change the function's tails to a new given end behavior. After a few students, the function might look something like this:

So the first student was asked to add a term in order to change the end behavior so that it rises to the left and falls to the right. The second student was then asked to add another term so that it rises to the left and to the right, etc.

I like using this calculator in class because the students can see how the graph changes as we change the output.

A final note...

One of my students showed me these hand motions and words (read from left to right) to go along with the end behaviors of polynomial functions. He remembered it from years ago, so it must have stuck! Maybe you've seen it before, but it was new to me. I can just see a classroom of students taking a test and moving their arms in the air as they try to answer a question...